The synthesis and processing of thermoplastics and thermoset polymeric materials rely on energy-inefficient and environmentally burdensome manufacturing methods. Frontal polymerization has emerged as an attractive, scalable alternative due to its exploitation of the heat of polymerization, which generally is wasted as unutilized heat-loss. The only external energy needed for frontal polymerization is an initial thermal (or photo) stimulus that locally ignites the reaction. The subsequent reaction exothermicity provides local heating; the transport of this thermal energy to neighboring monomers in either a liquid or gel-like state results in a self-perpetuating reaction zone that provides fully-cured polymeric thermosets and thermoplastics. Propagation of this polymerization front continues through the unreacted monomer media until either all reactants are consumed or sufficient heat-loss stalls further reaction. Several different polymerization mechanisms support frontal processes, including free-radical, cat- or anionic, amine-cure epoxides, and ring-opening metathesis polymerization. The choice of monomer, initiator/catalyst, and additives dictates how fast the polymer front traverses the reactant medium, as well as the maximum temperature achievable. Frontal polymerization enables the preparation of moldable thermoplastics derived from linear polymers. When crosslinking is involved, polymeric networks (e.g., rigid thermosets) are obtainable through a related process best described as a frontal curing reaction. Numerous applications of frontally-generated polymers and thermosets exist, ranging from the reinforcement of porous substrates to the design of patterned composite materials. In this review, we examine in detail the physical and chemical phenomena that govern frontal polymerization, as well as outline the existing applications.